line_3d_3.h

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//    |  /           |
//    ' /   __| _` | __|  _ \   __|
//    . \  |   (   | |   (   |\__ `
//   _|\_\_|  \__,_|\__|\___/ ____/
//                   Multi-Physics
//
//  License:         BSD License
//                   Kratos default license: kratos/license.txt
//
//  Main authors:    Riccardo Rossi
//                   Janosch Stascheit
//                   Felix Nagel
//  contributors:    Hoang Giang Bui
//                   Josep Maria Carbonell
//
 
#pragma once
 
// System includes
 
// External includes
 
// Project includes
#include "geometries/geometry.h"
#include "geometries/line_3d_2.h"
#include "integration/line_gauss_legendre_integration_points.h"
#include "integration/line_collocation_integration_points.h"
#include "utilities/integration_utilities.h"
#include "utilities/polynomial_utilities.h"
 
namespace Kratos
{
 
 
 
 
 
 
template<class TPointType>
 
class Line3D3 : public Geometry<TPointType>
{
public:
 
    typedef Geometry<TPointType> BaseType;
 
    KRATOS_CLASS_POINTER_DEFINITION( Line3D3 );
 
    typedef GeometryData::IntegrationMethod IntegrationMethod;
 
    typedef typename BaseType::GeometriesArrayType GeometriesArrayType;
 
    typedef TPointType PointType;
 
    typedef typename BaseType::IndexType IndexType;
 
 
    typedef typename BaseType::SizeType SizeType;
 
    typedef  typename BaseType::PointsArrayType PointsArrayType;
 
    typedef typename BaseType::IntegrationPointType IntegrationPointType;
 
    typedef typename BaseType::IntegrationPointsArrayType IntegrationPointsArrayType;
 
    typedef typename BaseType::IntegrationPointsContainerType IntegrationPointsContainerType;
 
    typedef typename BaseType::ShapeFunctionsValuesContainerType ShapeFunctionsValuesContainerType;
 
    typedef typename BaseType::ShapeFunctionsLocalGradientsContainerType ShapeFunctionsLocalGradientsContainerType;
 
    typedef typename BaseType::JacobiansType JacobiansType;
 
    typedef typename BaseType::ShapeFunctionsGradientsType ShapeFunctionsGradientsType;
 
    typedef typename BaseType::NormalType NormalType;
 
    typedef typename BaseType::CoordinatesArrayType CoordinatesArrayType;
 
 
    Line3D3( typename PointType::Pointer pFirstPoint, typename PointType::Pointer pSecondPoint,
             typename PointType::Pointer pThirdPoint )
        : BaseType( PointsArrayType(), &msGeometryData )
    {
        BaseType::Points().push_back( pFirstPoint );
        BaseType::Points().push_back( pSecondPoint );
        BaseType::Points().push_back( pThirdPoint );
    }
 
    Line3D3( const PointsArrayType& ThisPoints )
        : BaseType( ThisPoints, &msGeometryData )
    {
        if ( BaseType::PointsNumber() != 3 )
            KRATOS_ERROR << "Invalid points number. Expected 3, given " << BaseType::PointsNumber() << std::endl;
    }
 
    explicit Line3D3(
        const IndexType GeometryId,
        const PointsArrayType& rThisPoints
    ) : BaseType(GeometryId, rThisPoints, &msGeometryData)
    {
        KRATOS_ERROR_IF( this->PointsNumber() != 3 ) << "Invalid points number. Expected 3, given " << this->PointsNumber() << std::endl;
    }
 
    explicit Line3D3(
        const std::string& rGeometryName,
        const PointsArrayType& rThisPoints
    ) : BaseType(rGeometryName, rThisPoints, &msGeometryData)
    {
        KRATOS_ERROR_IF(this->PointsNumber() != 3) << "Invalid points number. Expected 3, given " << this->PointsNumber() << std::endl;
    }
 
    Line3D3( Line3D3 const& rOther )
        : BaseType( rOther )
    {
    }
 
    template<class TOtherPointType> Line3D3( Line3D3<TOtherPointType> const& rOther )
        : BaseType( rOther )
    {
    }
 
    ~Line3D3() override {}
 
    GeometryData::KratosGeometryFamily GetGeometryFamily() const override
    {
        return GeometryData::KratosGeometryFamily::Kratos_Linear;
    }
 
    GeometryData::KratosGeometryType GetGeometryType() const override
    {
        return GeometryData::KratosGeometryType::Kratos_Line3D3;
    }
 
 
    Line3D3& operator=( const Line3D3& rOther )
    {
        BaseType::operator=( rOther );
        return *this;
    }
 
    template<class TOtherPointType>
    Line3D3& operator=( Line3D3<TOtherPointType> const & rOther )
    {
        BaseType::operator=( rOther );
        return *this;
    }
 
 
    typename BaseType::Pointer Create(
        const IndexType NewGeometryId,
        PointsArrayType const& rThisPoints
        ) const override
    {
        return typename BaseType::Pointer( new Line3D3(NewGeometryId, rThisPoints ) );
    }
 
    typename BaseType::Pointer Create(
        const IndexType NewGeometryId,
        const BaseType& rGeometry
    ) const override
    {
        auto p_geometry = typename BaseType::Pointer( new Line3D3( NewGeometryId, rGeometry.Points() ) );
        p_geometry->SetData(rGeometry.GetData());
        return p_geometry;
    }
 
    Vector& LumpingFactors(
        Vector& rResult,
        const typename BaseType::LumpingMethods LumpingMethod = BaseType::LumpingMethods::ROW_SUM
        )  const override
    {
        if(rResult.size() != 3)
           rResult.resize( 3, false );
        rResult[0] = 1.0/6.0;
        rResult[2] = 2.0/3.0;
        rResult[1] = 1.0/6.0;
        return rResult;
    }
 
 
    double Length() const override
    {
        const IntegrationMethod integration_method = IntegrationUtilities::GetIntegrationMethodForExactMassMatrixEvaluation(*this);
        return IntegrationUtilities::ComputeDomainSize(*this, integration_method);
    }
 
    double Area() const override
    {
      return Length();
    }
 
 
    double DomainSize() const override
    {
        return Length();
    }
 
    bool IsInside(
        const CoordinatesArrayType& rPoint,
        CoordinatesArrayType& rResult,
        const double Tolerance = std::numeric_limits<double>::epsilon()
        ) const override
    {
        this->PointLocalCoordinates( rResult, rPoint );
 
        if ( std::abs( rResult[0] ) <= (1.0 + Tolerance) )
            return true;
 
        return false;
    }
 
    Vector& DeterminantOfJacobian( Vector& rResult, IntegrationMethod ThisMethod ) const override
    {
        const std::size_t number_of_integration_points = this->IntegrationPointsNumber( ThisMethod );
        if( rResult.size() != number_of_integration_points)
            rResult.resize( number_of_integration_points, false );
 
        Matrix J(3, 1);
        for (std::size_t pnt = 0; pnt < number_of_integration_points; ++pnt) {
            this->Jacobian( J, pnt, ThisMethod);
            rResult[pnt] = std::sqrt(std::pow(J(0,0), 2) + std::pow(J(1,0), 2) + std::pow(J(2,0), 2));
        }
        return rResult;
    }
 
    double DeterminantOfJacobian(
        IndexType IntegrationPointIndex,
        IntegrationMethod ThisMethod ) const override
    {
        Matrix J(3, 1);
        this->Jacobian( J, IntegrationPointIndex, ThisMethod);
        return std::sqrt(std::pow(J(0,0), 2) + std::pow(J(1,0), 2) + std::pow(J(2,0), 2));
    }
 
    double DeterminantOfJacobian( const CoordinatesArrayType& rPoint ) const override
    {
        Matrix J(3, 1);
        this->Jacobian( J, rPoint);
        return std::sqrt(std::pow(J(0,0), 2) + std::pow(J(1,0), 2) + std::pow(J(2,0), 2));
    }
 
 
    SizeType EdgesNumber() const override
    {
        return 2;
    }
 
    SizeType FacesNumber() const override
    {
        return 0;
    }
 
 
     Vector& ShapeFunctionsValues(
        Vector& rResult,
        const CoordinatesArrayType& rCoordinates
        ) const override
    {
        if(rResult.size() != 3) {
            rResult.resize(3, false);
        }
 
        rResult[0] = 0.5 * (rCoordinates[0] - 1.0) * rCoordinates[0];
        rResult[1] = 0.5 * (rCoordinates[0] + 1.0) * rCoordinates[0];
        rResult[2] = 1.0 - rCoordinates[0] * rCoordinates[0];
 
        return rResult;
    }
 
    double ShapeFunctionValue( IndexType ShapeFunctionIndex,
                                       const CoordinatesArrayType& rPoint ) const override
    {
        switch ( ShapeFunctionIndex )
        {
        case 0:
            return( 0.5*( rPoint[0] - 1.0 )*rPoint[0] );
        case 1:
            return( 0.5*( rPoint[0] + 1.0 )*rPoint[0] );
        case 2:
        return( 1.0 -rPoint[0]*rPoint[0] );
 
        default:
            KRATOS_ERROR << "Wrong index of shape function!" << *this << std::endl;
        }
 
        return 0;
    }
 
    virtual ShapeFunctionsGradientsType ShapeFunctionsLocalGradients(
        IntegrationMethod ThisMethod )
    {
        ShapeFunctionsGradientsType localGradients
        = CalculateShapeFunctionsIntegrationPointsLocalGradients( ThisMethod );
        const int integration_points_number
        = msGeometryData.IntegrationPointsNumber( ThisMethod );
        ShapeFunctionsGradientsType Result( integration_points_number );
 
        for ( int pnt = 0; pnt < integration_points_number; pnt++ )
        {
            Result[pnt] = localGradients[pnt];
        }
 
        return Result;
    }
 
    virtual ShapeFunctionsGradientsType ShapeFunctionsLocalGradients()
    {
        IntegrationMethod ThisMethod = msGeometryData.DefaultIntegrationMethod();
        ShapeFunctionsGradientsType localGradients
        = CalculateShapeFunctionsIntegrationPointsLocalGradients( ThisMethod );
        const int integration_points_number
        = msGeometryData.IntegrationPointsNumber( ThisMethod );
        ShapeFunctionsGradientsType Result( integration_points_number );
 
        for ( int pnt = 0; pnt < integration_points_number; pnt++ )
        {
            Result[pnt] = localGradients[pnt];
        }
 
        return Result;
    }
 
    Matrix& ShapeFunctionsLocalGradients( Matrix& rResult,
            const CoordinatesArrayType& rPoint ) const override
    {
        // Setting up result matrix
        if(rResult.size1() != 3 || rResult.size2() != 1) {
            rResult.resize( 3, 1, false );
        }
 
        noalias( rResult ) = ZeroMatrix( 3, 1 );
        rResult( 0, 0 ) =  rPoint[0] - 0.5;
        rResult( 1, 0 ) =  rPoint[0] + 0.5;
        rResult( 2, 0 ) = -rPoint[0] * 2.0;
        return( rResult );
    }
 
    Matrix& PointsLocalCoordinates( Matrix& rResult ) const override
    {
        if(rResult.size1() != 3 || rResult.size2() != 1) {
            rResult.resize( 3, 1, false );
        }
        noalias( rResult ) = ZeroMatrix( 3, 1 );
        rResult( 0, 0 ) = -1.0;
        rResult( 1, 0 ) =  1.0;
        rResult( 2, 0 ) =  0.0;
        return rResult;
    }
 
    CoordinatesArrayType& PointLocalCoordinates(
            CoordinatesArrayType& rResult,
            const CoordinatesArrayType& rPoint
            ) const override
    {
        // Define distance_objective as the gradient of ||point - global_coordinate(xi)||**2,
        // that is (point - local_coordinate(xi))*coordinate_derivative(xi) (times -2, which we ignore)
        // The zeros of the distance_objective are local extremes of the distance between point and line
        // We will get the zeros contained in the interval [-1, 1] (if any). If, for any of these zeros,
        // the point is on the line, the local coordinate is our result.
        rResult.clear();
 
        constexpr double TOLERANCE = 1e-12;
 
        const auto& r_p0 = this->GetPoint(0);
        const auto& r_p1 = this->GetPoint(1);
        const auto& r_p2 = this->GetPoint(2);
 
        // The method is prone to numerical instability close to the ends of the search interval
        // exit early in that case
        const array_1d<double,3> d0 = r_p0 - rPoint;
        if (MathUtils<double>::Dot3(d0, d0) < TOLERANCE) {
            rResult[0] = -1.0;
            return rResult;
        }
        const array_1d<double,3> d1 = r_p1 - rPoint;
        if (MathUtils<double>::Dot3(d1, d1) < TOLERANCE) {
            rResult[0] = 1.0;
            return rResult;
        }
 
        array_1d<double, 3> c1 = r_p0 + r_p1 - 2*r_p2;
        array_1d<double, 3> c2 = r_p1 - r_p0;
        array_1d<double, 3> c3 = r_p2 - rPoint;
 
        const double aux1 = MathUtils<double>::Dot3(c1, c1);
        if (aux1 < TOLERANCE) {
            // The geometry is a straight line, fall back to Line3D2.h
            auto line = Line3D2<TPointType>(
                this->pGetPoint(0), this->pGetPoint(1));
            return line.PointLocalCoordinates(rResult, rPoint);
        }
 
        const double aux2 = MathUtils<double>::Dot3(c1, c3);
        if (std::abs(aux2) < TOLERANCE) {
            // r_p2 == rPoint (we got the center of the line),
            //the local coordinate is 0
            return rResult;
        }
 
        PolynomialUtilities::PolynomialType distance_objective{
            0.5 * aux1,
            0.75 * MathUtils<double>::Dot3(c1, c2),
            0.25 * MathUtils<double>::Dot3(c2, c2) + aux2,
            0.5 * MathUtils<double>::Dot3(c2, c3)
        };
 
        std::vector<PolynomialUtilities::IntervalType> root_ranges;
        PolynomialUtilities::IsolateRoots(
            root_ranges, distance_objective,
            PolynomialUtilities::IntervalType{-1,1});
 
        Vector shape;
        for (const auto& interval: root_ranges) {
            double root = PolynomialUtilities::FindRoot(distance_objective, interval);
            // if point == line(root) we found our coordinate;
            rResult[0] = root;
            this->ShapeFunctionsValues(shape, rResult);
            array_1d<double,3> d = (shape[0]*r_p0 + shape[1]*r_p1 + shape[2]*r_p2) - rPoint;
            if (MathUtils<double>::Dot3(d, d) < TOLERANCE) {
                return rResult;
            }
        }
 
        // No points in the interval [-1,1] correspond to our local coordinate
        rResult[0] = 2.0;
        return rResult;
    }
 
    virtual Matrix& ShapeFunctionsGradients( Matrix& rResult, CoordinatesArrayType& rPoint )
    {
        if(rResult.size1() != 3 || rResult.size2() != 1) {
            rResult.resize( 3, 1, false );
        }
        noalias( rResult ) = ZeroMatrix( 3, 1 );
 
        rResult( 0, 0 ) =  rPoint[0] - 0.5;
        rResult( 1, 0 ) =  rPoint[0] + 0.5;
        rResult( 2, 0 ) = -rPoint[0] * 2.0;
        return rResult;
    }
 
 
    std::string Info() const override
    {
        return "1 dimensional line with 3 nodes in 3D space";
    }
 
    void PrintInfo( std::ostream& rOStream ) const override
    {
        rOStream << "1 dimensional line with 3 nodes in 3D space";
    }
 
    void PrintData( std::ostream& rOStream ) const override
    {
        // Base Geometry class PrintData call
        BaseType::PrintData( rOStream );
        std::cout << std::endl;
 
        // If the geometry has valid points, calculate and output its data
        if (this->AllPointsAreValid()) {
            Matrix jacobian;
            this->Jacobian( jacobian, PointType() );
            rOStream << "    Jacobian\t : " << jacobian;
        }
    }
 
 
protected:
 
 
 
 
 
 
 
private:
 
    static const GeometryData msGeometryData;
 
    static const GeometryDimension msGeometryDimension;
 
 
 
    friend class Serializer;
 
    void save( Serializer& rSerializer ) const override
    {
        KRATOS_SERIALIZE_SAVE_BASE_CLASS( rSerializer, BaseType );
    }
 
    void load( Serializer& rSerializer ) override
    {
        KRATOS_SERIALIZE_LOAD_BASE_CLASS( rSerializer, BaseType );
    }
 
    Line3D3(): BaseType( PointsArrayType(), &msGeometryData ) {}
 
 
 
    static Matrix CalculateShapeFunctionsIntegrationPointsValues( typename BaseType::IntegrationMethod ThisMethod )
    {
        const IntegrationPointsContainerType& all_integration_points = AllIntegrationPoints();
        const IntegrationPointsArrayType& IntegrationPoints = all_integration_points[static_cast<int>(ThisMethod)];
        int integration_points_number = IntegrationPoints.size();
        Matrix N( integration_points_number, 3 );
 
        for ( int it_gp = 0; it_gp < integration_points_number; it_gp++ )
        {
            double e = IntegrationPoints[it_gp].X();
            N( it_gp, 0 ) = 0.5 * ( e - 1 ) * e;
            N( it_gp, 2 ) = 1.0 - e * e;
            N( it_gp, 1 ) = 0.5 * ( 1 + e ) * e;
        }
 
        return N;
    }
 
    static ShapeFunctionsGradientsType CalculateShapeFunctionsIntegrationPointsLocalGradients(
        typename BaseType::IntegrationMethod ThisMethod )
    {
        const IntegrationPointsContainerType& all_integration_points = AllIntegrationPoints();
        const IntegrationPointsArrayType& IntegrationPoints = all_integration_points[static_cast<int>(ThisMethod)];
        ShapeFunctionsGradientsType DN_De( IntegrationPoints.size() );
        std::fill( DN_De.begin(), DN_De.end(), Matrix( 3, 1 ) );
 
        for ( unsigned int it_gp = 0; it_gp < IntegrationPoints.size(); it_gp++ )
        {
            Matrix aux_mat = ZeroMatrix(3,1);
            const double e = IntegrationPoints[it_gp].X();
            aux_mat(0,0) = e - 0.5;
            aux_mat(2,0) = -2.0 * e;
            aux_mat(1,0) = e + 0.5;
            DN_De[it_gp] = aux_mat;
        }
 
        return DN_De;
    }
 
    static const IntegrationPointsContainerType AllIntegrationPoints()
    {
        IntegrationPointsContainerType integration_points = {{
                Quadrature<LineGaussLegendreIntegrationPoints1, 1, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature<LineGaussLegendreIntegrationPoints2, 1, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature<LineGaussLegendreIntegrationPoints3, 1, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature<LineGaussLegendreIntegrationPoints4, 1, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature<LineGaussLegendreIntegrationPoints5, 1, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature<LineCollocationIntegrationPoints1, 1, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature<LineCollocationIntegrationPoints2, 1, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature<LineCollocationIntegrationPoints3, 1, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature<LineCollocationIntegrationPoints4, 1, IntegrationPoint<3> >::GenerateIntegrationPoints(),
                Quadrature<LineCollocationIntegrationPoints5, 1, IntegrationPoint<3> >::GenerateIntegrationPoints()
            }
        };
        return integration_points;
    }
 
    static const ShapeFunctionsValuesContainerType AllShapeFunctionsValues()
    {
        ShapeFunctionsValuesContainerType shape_functions_values = {{
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsValues( GeometryData::IntegrationMethod::GI_GAUSS_1 ),
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsValues( GeometryData::IntegrationMethod::GI_GAUSS_2 ),
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsValues( GeometryData::IntegrationMethod::GI_GAUSS_3 ),
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsValues( GeometryData::IntegrationMethod::GI_GAUSS_4 ),
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsValues( GeometryData::IntegrationMethod::GI_GAUSS_5 ),
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsValues( GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_1 ),
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsValues( GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_2 ),
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsValues( GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_3 ),
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsValues( GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_4 ),
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsValues( GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_5 )
            }
        };
        return shape_functions_values;
    }
 
    static const ShapeFunctionsLocalGradientsContainerType AllShapeFunctionsLocalGradients()
    {
        ShapeFunctionsLocalGradientsContainerType shape_functions_local_gradients = {{
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_GAUSS_1 ),
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_GAUSS_2 ),
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_GAUSS_3 ),
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_GAUSS_4 ),
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_GAUSS_5 ),
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_1 ),
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_2 ),
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_3 ),
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_4 ),
                Line3D3<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients( GeometryData::IntegrationMethod::GI_EXTENDED_GAUSS_5 )
            }
        };
        return shape_functions_local_gradients;
    }
 
 
 
 
 
 
    template<class TOtherPointType> friend class Line3D3;
 
 
 
}; // Class Geometry
 
 
 
 
 
 
template<class TPointType>
inline std::istream& operator >> ( std::istream& rIStream,
                                   Line3D3<TPointType>& rThis );
 
template<class TPointType>
inline std::ostream& operator << ( std::ostream& rOStream,
                                   const Line3D3<TPointType>& rThis )
{
    rThis.PrintInfo( rOStream );
    rOStream << std::endl;
    rThis.PrintData( rOStream );
 
    return rOStream;
}
 
 
 
template<class TPointType>
const GeometryData Line3D3<TPointType>::msGeometryData(
        &msGeometryDimension,
        GeometryData::IntegrationMethod::GI_GAUSS_2,
        Line3D3<TPointType>::AllIntegrationPoints(),
        Line3D3<TPointType>::AllShapeFunctionsValues(),
        AllShapeFunctionsLocalGradients() );
 
template<class TPointType>
const GeometryDimension Line3D3<TPointType>::msGeometryDimension(3, 1);
 
}  // namespace Kratos.